Nov 12 - Very Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R1C3 is the only square in row 1 that can be <5>
R2C8 is the only square in row 2 that can be <2>
R3C9 is the only square in row 3 that can be <5>
R5C5 is the only square in row 5 that can be <2>
R8C8 is the only square in row 8 that can be <7>
R7C2 is the only square in column 2 that can be <9>
R7C1 is the only square in row 7 that can be <5>
R4C2 is the only square in row 4 that can be <5>
R4C1 is the only square in row 4 that can be <1>
R3C1 can only be <4>
R3C2 can only be <1>
Squares R2C2 and R2C3 in row 2 form a simple naked pair. These 2 squares both contain the 2 possibilities <67>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R2C6 - removing <7> from <479> leaving <49>
Squares R5C1 and R6C1 in block 4 form a simple naked pair. These 2 squares both contain the 2 possibilities <36>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R5C3 - removing <6> from <467> leaving <47>
R6C2 - removing <6> from <467> leaving <47>
Intersection of block 3 with column 7. The value <3> only appears in one or more of squares R1C7, R2C7 and R3C7 of block 3. These squares are the ones that intersect with column 7. Thus, the other (non-intersecting) squares of column 7 cannot contain this value.
R5C7 - removing <3> from <369> leaving <69>
Squares R3C5 and R3C8 in row 3 and R6C5 and R6C8 in row 6 form a Simple X-Wing pattern on possibility <9>. All other instances of this possibility in columns 5 and 8 can be removed.
R9C5 - removing <9> from <14689> leaving <1468>
Squares R3C5 and R3C8 in row 3, R4C8 and R4C9 in row 4 and R7C5, R7C8 and R7C9 in row 7 form a Swordfish pattern on possibility <8>. All other instances of this possibility in columns 5, 8 and 9 can be removed.
R1C5 - removing <8> from <178> leaving <17>
R9C5 - removing <8> from <1468> leaving <146>
Squares R5C1, R6C1, R5C9 and R6C9 form a Type-2 Unique Rectangle on <36>.
R4C9 - removing <7> from <78> leaving <8>
R4C8 can only be <4>
R4C5 can only be <7>
R1C5 can only be <1>
R1C4 can only be <3>
R1C7 can only be <8>
R1C6 can only be <7>
R3C8 can only be <9>
R3C5 can only be <8>
R6C8 can only be <3>
R2C7 can only be <3>
R6C1 can only be <6>
R7C8 can only be <8>
R7C5 can only be <6>
R6C9 can only be <7>
R5C1 can only be <3>
R6C2 can only be <4>
R5C9 can only be <6>
R7C9 can only be <3>
R9C5 can only be <4>
R6C5 can only be <9>
R5C7 can only be <9>
R8C2 can only be <6>
R5C3 can only be <7>
R8C7 can only be <1>
R2C2 can only be <7>
R9C3 can only be <8>
R8C4 can only be <5>
R9C7 can only be <6>
R9C6 can only be <9>
R8C3 can only be <4>
R9C4 can only be <1>
R2C6 can only be <4>
R2C3 can only be <6>
R2C4 can only be <9>
R5C6 can only be <5>
R5C4 can only be <4>
R8C6 can only be <8>
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